We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Geometry and Topology Seminar: The prescribed Weingarten curvatures problem in hyperbolic space

Presented by Daniel Ballesteros-Chavez, Durham

18 January 2018 13:00 in CM221

We will present a detailed proof for the existence of a closed convex hypersurface in the hyperbolic ball with prescribed 1 \le k < n - Weingarten curvature. Specifically, we deal with the equivariant problem for a sufficiently large group of hyperbolic automorhphisms. The proof proceeds by establishing (nonlinear) strict ellipticity of the associated PDE. Then we obtain existence in C^{1,a} for an auxiliary problem by Schauder theory, C^2 smoothness using ellipticity and a Lemma by Cheng-Yau, and C^{2,a} - regularity by Evans-Krylov. Finally, existence of a solution is established by degree theory in the equivariant setting. The results presented are part of the speakers PhD thesis.

Contact or or for more information